In this study, we clarified that electric fields, plasma rotation, and compressibility are closely related to the suppression mechanism of turbulent transport in a complex system of magnetohydrodynamic (MHD) flow. The findings are summarized as follows.(1) In tokamak's high-confinement (H) modes, the turbulent transport was shown to be suppressed through the electric field near the separatrix, specifically, its curvature, in contrast with the previous finding based on the radial electric shear.(2) In the turbulent-transport suppression, the ratio of the renormalized density variance to the turbulent Mach number was shown to be a critical parameter. In order to deal with compressibility effects accurately, it is necessary to distinguish between acoustic density fluctuations and those arising from entropy fluctuations. For this purpose, a turbulence model consisting of the transport equations for the turbulent energy, its dissipation rate, the compressible part of the turbulent energy, and the entropy variance was constructed usign a two-scale direct-interaction formalism.(3) The concept of turbulent cross helicity was introduced as a quantity connecting plasma rotation with magnetic fields. Using the concept, it was confirmed that global plasma motion and frame rotation result in the formation of global magnetic fields, and that this mechanism is closely associated with the suppression of turbulent transport in a MHD system. These findings were discussed in the context of H modes in tokamaks and the generation of magnetic fields in accretion disks as well as the occurrence of their bipolar jets.